Introduction to Combinatorics by Erickson, Martin J. -- Read -- Imperial Library of Trantor

Index

Cover Half Title page Title page Copyright page Dedication Preface Chapter 1: Basic Counting Methods

1.1 The multiplication principle 1.2 Permutations 1.3 Combinations 1.4 Binomial coefficient identities 1.5 Distributions 1.6 The principle of inclusion and exclusion 1.7 Fibonacci numbers 1.8 Linear recurrence relations 1.9 Special recurrence relations 1.10 Counting and number theory Notes

Chapter 2: Generating Functions

2.1 Rational generating functions 2.2 Special generating functions 2.3 Partition numbers 2.4 Labeled and unlabeled sets 2.5 Counting with symmetry 2.6 Cycle indexes 2.7 Pólya’s theorem 2.8 The number of graphs 2.9 Symmetries in domain and range 2.10 Asymmetric graphs Notes

Chapter 3: The Pigeonhole Principle

3.1 The principle 3.2 The lattice point problem and SET® 3.3 Graphs 3.4 Colorings of the plane 3.5 Sequences and partial orders 3.6 Subsets Notes

Chapter 4: Ramsey Theory

4.1 Ramsey’s theorem 4.2 Generalizations of Ramsey’s theorem 4.3 Ramsey numbers, bounds, and asymptotics 4.4 The probabilistic method 4.5 Schur’s theorem 4.6 Van der Waerden’s theorem Notes

Chapter 5: Error-Correcting Codes

5.1 Binary codes 5.2 Perfect codes 5.3 Hamming codes 5.4 The Fano Configuration Notes

Chapter 6: Combinatorial Designs

6.1 t-designs 6.2 Block designs 6.3 Projective planes 6.4 Latin squares 6.5 MOLS and OODs 6.6 Hadamard matrices 6.7 The Golay code and S(5, 8, 24) 6.8 Lattices and sphere packings 6.9 Leech’s lattice Notes

Appendix A: Web Resources Appendix B: Notation Exercise Solutions References Index